Saturday, April 30, 2011

Down to Glastonbury this afternoon, Clare and myself in the car; Alex and Adrian cycling. There's a narrow path up the north-east slope of the Tor, less climbing than on the main route from the town but quite exposed, high on the steep, grassy slope. Today the wind was trying to whip us off. How brave we were: we even took the same precipitous route going down!

Prior to this excitement, Adrian borrowed my camera phone to take some snaps of Wells: instant nostalgia before returning to Canada. His first stop was the Falklands Island shop pictured.

How can this be a viable business? It's obviously a front for the SIS.

Wells town market was buzzing today. If this is what it's like at the end of April, it will be a colloidal soup of humanity in the summer.

Finally, here's a practice shot he took of us on the couch.

I've been working hard at decoherence. I've grasped that it's all to do with superpositions entangling with the environment and the differing phases of the superposition thereby losing phase coherence. I have not yet succeeded in integrating this understanding with the treatment of mixed states using the density matrix/operator.

Trouble is, the material on the net is not really suitable for self-study: it assumes someone already outlined the conceptual connections and did a few examples, so the texts simply provide the formal derivations. They're not difficult but I keep asking myself, 'what does it really mean in the physics?'

Thursday, April 28, 2011

Just a brief flashback to the first day Alex arrived (Bank Holiday Friday April 22nd) when clutching his new helicopter, still unpacked, he chanced upon the cat inspecting the last flying thing it had encountered. Yes, the little brown sparrow pictured was quite dead.

It's a dead bird (and a helicopter)

Over the last few days we have been taking it easy. Monday/Tuesday my mother visited; yesterday I was in London to meet with a client. Today we decided on the Cheddar Gorge clifftop walk. We parked at the top end of the gorge and ascended the south side to begin the walk towards Cheddar.

Alex and Adrian (in red) at Cheddar Gorge

Once you get on the top up a steep, rocky path there are some scary overlooks down the cliffs. Here Alex and Adrian (in red) are exploring a pinacle.

Cheddar Reservoir (with Clare)

There are also good views looking west towards Brean Down and the sea at Burnham, with Cheddar reservoir in the foreground.

As we passed Jacob's Ladder, five minutes from the pub, someone had to retrace our steps and go fetch the car. I enjoyed the 50 minute walk back, almost all of it uphill in the sunshine. There is a curious ascetic experience to be tired in every fibre of your body as you endlessly climb.

Clare had further confirmation this morning: a CT scan first thing Tuesday morning and a meeting Wednesday morning, both at Taunton.

Just a final thought on AV. It's interesting how neither the YES nor the NO camp can be honest about their respective cases. E.O Wilson, world authority on sociobiology and ants once quipped on Marxism: 'great theory, wrong species'. The most profound judgement in four words.

There might be a species for which iterated rounds of voting produced the optimal choice of political strategies in elections but human beings are not it. Consider the following case. The status quo isn't working and there are two credible strategies for dealing with it.

- Strategy A, advocated by party A, wants to lower debt by cutting public spending.

- Strategy B, advocated by party B, wants to keep demand up and retain employment and service levels by borrowing even more, repaying later.

In a particular seat, party A's supporters provide 40% of the vote, party B's supporters provide 35% of the vote.

What about the remaining 25%? They support the LaLa party which believes that banks should be abolished, the minimum wage should be raised to £25,000 per year and no-one should be allowed to earn more than this. They calculate that the resources this would free up would allow both public employment and services to be massively increased and the debt would be a non-issue.

Under first past the post, party A will win and will get a chance to implement their policy ... which is rational if not widely popular. Under other circumstances party B might win and execute their policy, which is also rational and could work. If either policy fails to work, it at least has the benefits of clarity and there is an opportunity to learn the appropriate lessons and move on.

However, under AV the supporters of the LaLa party get a chance to vote in the second round after their candidate is eliminated. In fact they will decide the result. Unfortunately it is now rational for both party A and party B to blur their strategies to appeal to the economically-illiterate and utopian LaLa 25%. We no longer have clarity about rational strategies for running and fixing an advanced capitalist economy.

Now, the blurring of messages to appeal to a wider electorate happens all the time of course, and we are the worse for it. However, AV just makes it worse.

You see the problem. We are not all identical clones sitting in a Platonic command cubicle making wise decisions for the greater good of the community: that's ants. We are special-interest tribes with appropriate strategies, some of which are aligned with the art of the possible (while favouring one interest group over another of course) while some are simply idiotic and would fly any economy into the ground.

It's important not to blur the options and it's important to be able to identify (sooner or later) leadership teams and strategies which actually work. Fuzziness, group-hugs in the name of sacred 'democracy', and general niceness all round doesn't necessarily cut it.

However, you won't hear the argument above put forward by either side in the run-up to May 5th. It would offend the LaLa voters and that would never do if you want to win.

Wednesday, April 20, 2011

Today Adrian and myself visited my mother in Bristol and after lunch at the Almondsbury Garden Centre we took advantage of the summery afternoon to drive to Severn Beach. Years ago, Adrian and Alex as toddlers were rescued from the deep estuary mud by a man in waders. They were washed in the sink of the public toilets and wrapped in bin bags to be taken to my parents' home for a proper bath.

Since those halcyon days they have built an enormous bridge (the M4 second Severn crossing) which now dominates the seafront view pictured below ... but the mud is still there.

Adrian and his Grandmother at Severn Beach

The M4 second Severn crossing

There have been better times

When I was little myself we used to come to Severn Beach in the summer: there was a little funfair at the end of the front. Now look at it! So insignificant that it hasn't even been vandalised!

Adrian simulating an asteroid impact at Severn Beach

So here we see the true nature of the mud as Adrian continues his youthful interest in throwing stones into the mud to see what will happen.

Yesterday I had to travel to London for a late morning meeting with a client. A long day as the train developed a fault coming back and we sat around for forty minutes divided equally between Pewsey and Westbury, Wilts. I only mention this everyday irritant as an indicator that the trains are just not reliable.

Monday, April 18, 2011

A certain amount of continuing excitement in the theoretical physics community following the recent report from the Tevatron at Fermilab that a new fundamental particle might have been discovered. This would not be the Higgs (the decay route is all wrong) but might be a new force boson, the Z'.

Saturday, April 16, 2011

Adrian arrived here in Wells today after a six hour train ride from Liverpool. He landed in the UK at Manchester on Thursday very early and then spent some time in the area visiting relatives. He's here till his Canadian Visa comes through, then off to Whistler.

Currently working on a review of a gem of a book (mentioned in a previous post), Essential Quantum Mechnics by Gary Bowman. This is standard non-relativistic QM as you would meet it in an advanced undergraduate course, but considered from a sophisticated conceptual standpoint. It is given that the reader has 'got' the formal results; Gary is interested in what exactly the maths means in a broader conceptual context.

I think I will write a vanilla, down-the-line review for Amazon and a more elaborated, SF version for sciencefiction.com.

Wednesday, April 13, 2011

I received a note today from Dylan H. who works in defence R&D. She's studying quantum theory with the Open University and wrote:

"I read your blog from 2009 on QM SM358 having had my interest prompted on a Google search. I’m currently doing this same course and am already freaking out about the exam in October – do you have any study/revision tips you could pass on?"___

"Hope you're finding the course interesting. I've subsequently been looking at Quantum Field Theory and found the OU course an excellent preparation. The exam is straightforward if you know the material but it DOES reward time assigned to revision.

My own approach was to read through the entire course again, all three volumes, doing the inline questions where I felt any puzzlement. It's amazing how much clearer it seems second time round. There was also a web-based series of revision tests which I faithfully did and although I found them both stressful and irritating they were worth it.

I assume you attended the summer school. If so, you will have been given a number of question papers together with the answers. I did these systematically as part of my revision.

Finally, one of the key issues in a beginning QM course is to figure out the many confusing concepts. SM358 doesn't do a particularly bad job at conceptual clarity [e.g. distinguishing between operators, eigenvectors, eigenvalues, amplitudes, superpositions, representations, observables, ...] but it sometimes helps to have a complementary book. My choice would be Essential Quantum Mechanics by Gary Bowman which focuses relentlessly on the key concepts and you might find it helpful too.

About a week before the exam I worked through three past papers under semi-exam conditions (I made sure I attempted ALL the questions where there were options). I did get a distinction, so I guess the answer is (i) revise ALL the material; (ii) do lots of questions, don't just read stuff."

To my embarrassment I then had to write her a follow-up email:

"In my haste to reply to you before dinner, I omitted to notice that you're just starting out on the course. Let me therefore add:

1. The course is very conceptually demanding in the first few months. If you feel you will never understand it, don't worry, I felt just the same. Stick at it and immerse yourself and it WILL become clearer by June!

2. Go to the Summer School.

3. The book I recommended is great to read in September when you’ve completed Book 2 of the course. It won't make a lot of sense at this stage and it's a waste of your time and money to look at it now. It's use is in revision for a 'second opinion' on the conceptual foundations.

Best,

Nigel."

---

We were in Taunton today, about an hour's ride from Wells. The expected torrential rain did not materialise but on the way back we saw a wind turbine spinning at a fantastic rate. It might, however, have been the result of the low-flying Chinook which was powering over the Somerset Levels dressed in its best camo. I'm glad they've finally got the software bugs out of that machine ...

Monday, April 11, 2011

Following a publishing glitch, my review of the hard-SF short-story collection Engineering Infinity has now been posted at sciencefiction.com.

The Old Bristol Road from Wells to Bristol is charmingly rustic, running alongside Chew Valley Lake and entering Bristol via a steep descent at Dundry. It took us less than an hour to get to the Cribbs Causeway Vue where we enjoyed 'Source Code'. Here's how Wikipedia describes the start of the story.

"Captain Colter Stevens (Jake Gyllenhaal) is a decorated army helicopter pilot whose last memory is of his recent mission in Afghanistan, flying with his team while taking on enemy gunfire. He awakens on a train headed for Chicago with no memory of how he arrived there. His reflection is of a different man and his wallet says his name is Sean Fentress. Sitting across from him is a woman named Christina Warren (Michelle Monaghan) who seems to know him as history teacher Sean Fentress. Before he can understand what is happening, a bomb goes off and destroys the train."

It turns out that Colter is within a simulation based on the memories of the last eight minutes of Sean Fentress's life. He is sent back again and again into those memories with a mission to find the bomb and the bomber to avert an even greater threat to Chicago. To Colter's surprise, the simulation is malleable: as he relives the train experience he learns the sequence of events and can act to change it: recurrences are different every time. Is this just a simulation, as the Source Code mission team seems to believe, or is he occupying alternate histories of the quantum multiverse? (What do you think?)

Although a couple of people (obviously of little imagination) walked out before the end, we thought the film was great. It's thought-provoking and exciting in equal measure and it even manages to end happily - amazing for a movie where everything is based on damage and death.

Sunday, April 10, 2011

Yesterday morning the sun beautifully illuminated the daffodils in our front hall. When Clare saw it she was impelled to turn it into a big image. After much arithmetic, we were able to print out six blown-up jigsaw pieces and she set to work.

Here is the artist trimming and arranging and glueing onto a cardboard backing.

And here is the result in its chosen location, waiting for some final trimming tomorrow.

Thursday, April 07, 2011

We're blessed by some wonderful walks here in the Mendips. This afternoon we parked at the top end of the Cheddar Gorge and walked up the path through Black Rock and into Long Wood. We came back via Velvet Bottom: a couple of pictures of myself and Clare on the way back down.

When I bought my ASUS Netbook last Saturday the salesperson at the Cribbs Causeway PC World store looked at me sharply and said, "You do have a proper computer don't you, as well?" At the time I thought this was a curious point but now I understand what he meant.

The Netbook, running Windows 7 starter, is just fine. Configuring it has taken a couple of days (see previous post) but really presented few problems. The trouble is inherent in a design which costs just a couple of hundred pounds, uses a low-power processor and utilises just 1 GB of RAM.

The machine is midway between a serious device and a toy. It can do everything but it's just so slow! And just a bit brittle as compared to the robust HP laptop which I'm using to write this post. Still, it's just 1 kg and runs for ages on its battery; ideal for travelling around.

When we first moved into our new house in the winter of last year, we were unable to light the gas fire (the pilot had been switched off). I made frantic phone calls to the previous owners and eventually got instructions. Ever since I have been haunted by the thought that come next winter we will have forgotten again how to light it.

I therefore coerced Clare this afternoon into showing me how to do it (video above). Naturally we messed it up.

Wednesday, April 06, 2011

Here's Clare discussing the good news this afternoon with him. Adrian is due back here from Canada some time next week.

We had the electrician in today to replace our tentacled mess of nested power bars with proper office-like sockets (below). They did some other work too including installing the lighting set above in the upstairs and downstairs halls.

We seem to be overrun by laptops according to the picture above. On the left is my new ASUS Netbook, bought for client presentations and on-site working to replace the Advent Notebook on the right whose fan died some months ago.

All done without a hitch although I have a residual issue with downloading a free email client and configuring it to connect with Pro4's IMAP mail server. The above has taken two calendar days so far ...

Monday, April 04, 2011

One of the most foundational concepts in physics is Noether's theorem, which states that symmetries of the laws of nature mathematically imply conserved quantities. Thus conservation of energy is revealed as a logical consequence of the fact that the laws of physics are timeshift-invariant; conservation of momentum is similarly understood to be a consequence of the spatial-translation invariance of the laws of physics. More abstract symmetries (gauge symmetries) imply such things as the conservation of electrical charge.

John Baez in 2002 gave the 'simplest possible proof' of Noether's theorem which I reproduce below. It repays attention as the concepts are quite subtle even though the maths is sixth-form level.

---

Note that some of the derivatives below are partial but for simplicity they are all shown with 'd'.

Suppose we have a particle able to move on a line with position x and velocity v = dx/dt under the influence of a potential V(x). Note that both x(t) and v(t) are functions of time t.

The Lagrangian is L = KE - PE = (1/2) mv2 - V(x).

The momentum of the particle is p = mv = dL/dv.

The force (caused by the potential) on the particle is F = -dV/dx = dL/dx.

The Euler-Lagrange equation (derived from the principle of least action) says that dL/dx = d/dt(dL/dv), so working it out:

Now we suppose that the Lagrangian has a symmetry defined by a parameter s, so that if there is a transformation which sends x (at some t) to some new position x(s) (at time t) then the Lagrangian is unchanged. Note that this makes both x and v now functions of t and s: x(t, s) and v(t, s). I will often suppress one or both of these arguments for notational declutter.

As the Lagrangian is unchanged by the application of s, this means:

dL(x(t, s), v(t, s))/ds = 0.

With less clutter we can write dL(x, v)/ds = 0.

The symmetry might, for example, be: xt(s) -> xt + s which simply shifts the particle at xt spatially by amount s (at every time point). This corresponds to doing the experiment again in a different part of the lab.

Or xt(s) -> xt+s which shifts the particle at (x, t) through time by time-increment s. This corresponds to doing the experiment in the afternoon rather than the morning.

So here is the proposed conserved quantity: pdx(s)/ds.

Examples

We assume that the potential V(x) = 0 so there are no applied forces (which makes the conservation law simpler). In the first example, dx(s)/ds = d(xt + s)/ds = 1 (as t is held constant). So pdx(s)/ds = p. This says that momentum is the conserved quantity in space translation.

In the second example, we hold t constant and let s do the job of incrementing time. Define a new t-coordinate t' = t + s, noting that dt'/ds = 1.

Then dx(s)/ds = (dx/dt')(dt'/ds) = dx/dt' = v so

pdx(s)/ds = pv = 2 * (1/2)mv2 which shows that the particle's energy is what will be conserved in time translation.

Proof

Differentiate the allegedly conserved quantity pdx(s)/ds with respect to t. [Conservation of anything means conservation as time passes].

(dp/dt)(dx(s)/ds) + pd[dx(s)/ds]/dt =

(dp/dt)(dx(s)/ds) + pdv(s)/ds ... assuming s is time-independent.

Now we replace p and its derivatives by their Lagrangian equivalents.

(dL/dx)(dx/ds) + (dL/dv)(dv/ds) = dL(x, v)/ds by the chain rule.

But dL/ds = 0 as transformations via s are a symmetry of L, so the conserved quantity pdx(s)/ds is indeed conserved, as Emmy Noether indicated.

As Elaine and myself were clearing my mother's front bedroom over the weekend prior to painting it, I came across this.

This picture of a very gawky teenage-me with my mother in our back garden in Henbury, Bristol is probably from the mid-sixties. It testifies to a lifelong addiction to jeans, cardigans and rolled-up sleeves; I'm probably wearing sandals too. You just can't suppress the essential geek.

Saturday, April 02, 2011

Normally I never do interior decoration: my job is to hunt woolly mammoths while Clare sorts out things like painting and decorating. Still, one has to rise to these challenges.

I discovered that painting walls and ceilings is paintbrush stuff around the edges and rollering in the middle. If, like me, you basically want to chuck as much paint as possible onto the wall in the shortest possible time, you absolutely soak the roller in paint. Then, as it spins, it throws off a fine pink mist which covers your arm. There, isn't that interesting? Don't you think that the result (above) is actually rather purple?

After more than a year, building work on our house in Wells is coming to an end. Except, that is, for the area outside the back door (pictured above) which was the interior of a 'utility lean-to' for the previous owner. It desperately needs resurfacing and proper drainage, a project for the warmer weather.

This note of odds-and-ends would not be complete without an update on the Amaryllis, which has beautifully flowered while not failing to exhibit a darker, more suggestive side.